Volume 9, issue 1 (2009)

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Graphs of subgroups of free groups

Larsen Louder and D B McReynolds

Algebraic & Geometric Topology 9 (2009) 327–335
Abstract

We construct an efficient model for graphs of finitely generated subgroups of free groups. Using this we give a very short proof of Dicks’s reformulation of the strengthened Hanna Neumann Conjecture as the Amalgamated Graph Conjecture. In addition, we answer a question of Culler and Shalen on ranks of intersections in free groups. The latter has also been done independently by R P Kent IV.

Keywords
folding, free groups, Hanna Neumann conjecture
Mathematical Subject Classification 2000
Primary: 20E05
References
Publication
Received: 27 August 2008
Revised: 25 January 2009
Accepted: 28 January 2009
Published: 23 February 2009
Authors
Larsen Louder
Department of Mathematics
University of Michigan
Ann Arbor, MI 48109-1043
USA
http://www.math.lsa.umich.edu/~llouder/
D B McReynolds
Department of Mathematics
University of Chicago
Chicago, IL 60637
USA
http://www.math.uchicago.edu/~dmcreyn/